curved manifold

A smoothly varying lower-dimensional surface in activation space that captures a concept better than a straight linear direction.

Neighborhood — ranked by edge-count

claim

Curved manifolds often represent concepts better than linear directions.
cites
Proposes that nonlinear geometric structure is superior to linear feature spaces for capturing semantic content.

concept

manifold
related_to
A smooth, potentially curved surface in activation space along which activations vary according to a coherent semantic dimension.

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

One-dimensional Manifoldconcept0.805
The type of manifold fitted to the cyclic concept structure in both activation and behavior space — a path along which steering moves the model.
manifold-level descriptionconcept0.766
An interpretability approach that describes representations in terms of entire curved manifolds rather than many small features.
Feature Manifoldsframework0.762
Hypothesized extension of superposition where features may be higher-dimensional manifolds rather than 1D directions
1D manifoldconcept0.759
A single-continuous curve in activation space encoding a single variable, such as car position in the Mountain Car case.
Geometryconcept0.755
The actual shapes and spatial relationships of buildings, essential to living structure.
behavior manifoldconcept0.755
One-dimensional curved surface in output probability space; the paper shows this mirrors representation manifold structure.
manifold learningframework0.750
Technique used to fit M_h and M_y from data; enables manifold steering.
representation manifoldconcept0.739
One-dimensional curved surface in internal activation space; the paper demonstrates alignment with behavior manifold.